[5] A promising youth rider, Skjelmose finished in top positions in junior categories of major races, and won the Tour du Pays de Vaud in 2018.

Shortly after, he had a setback after receiving a ten-month suspension due to a doping test revealing traces of the performance-enhancing drugs originating from dietary supplements.

On 26 May 2018, Skjelmose won an individual time trial in the Tour du Pays de Vaud, and later that same day, he also finished 22nd in a regular road stage.

[8] On 26 May 2018, during the Tour du Pays de Vaud, a doping test conducted on Skjelmose revealed traces of the substance methylhexanamine, a performance-enhancing drug prohibited during competitions.

[16] On 19 April 2023, Skjelmose finished in second place at La Flèche Wallonne, at the top of the Mur de Huy, just behind Tadej Pogačar.

[21] His performances in the 2023 season were praised by Lance Armstrong: "If you're talking all day long about Vingegaard and Pogačar, who's number three... boy, I feel like he's gonna start trickling into the top.